Pasquale Di Bari

Flavour effects on leptogenesis predictions

Flavor effects in leptogenesis reduce the region of the see-saw parameter space where the final predictions do not depend on the initial conditions, the strong wash-out regime. In this case we show that the lowest bounds holding on the lightest right-handed (RH) neutrino mass and on the reheating temperature for hierarchical heavy neutrinos, do not get relaxed compared to the usual ones in the one-flavor approximation, M_1 (T_reh) \gtrsim 3 (1.5) x 10^9 GeV. Flavor effects can however relax down to these minimal values the lower bounds holding for fixed large values of the decay parameter K_1. We discuss a relevant definite example showing that, when the known information on the neutrino mixing matrix is employed, the lower bounds for K_1 \gg 10, are relaxed by a factor 2-3 for light hierarchical neutrinos, without any dependence on \theta_13 and on possible phases. On the other hand, going beyond the limit of light hierarchical neutrinos and taking into account Majorana phases, the lower bounds can be relaxed by one order of magnitude. Therefore, Majorana phases can play an important role in leptogenesis when flavor effects are included.

The minimal scenario of leptogenesis

We review the main features and results of thermal leptogenesis within the type I seesaw mechanism, the minimal extension of the Standard Model explaining neutrino masses and mixing. After presenting the simplest approach, the vanilla scenario, we discuss various important developments of recent years, such as the inclusion of lepton and heavy neutrino flavour effects, a description beyond a hierarchical heavy neutrino mass spectrum and an improved kinetic description within the density matrix and the closed-time-path formalisms. We also discuss how leptogenesis can ultimately represent an important phenomenological tool to test the seesaw mechanism and the underlying model of new physics.

New aspects of leptogenesis bounds

We present a general analysis that reveals new aspects of the leptogenesis bounds on neutrino masses and on the reheat temperature of the Universe. After revisiting a known effect coming from an unbounded term in the total CP asymmetry, we show that an unbounded term in the flavored CP asymmetries has a stronger impact. It relaxes the lower bound on the reheat temperature down to 10^8 GeV for (M_2-M_1)/M_1=O(1-100) and for a mild tuning of the parameters in the see-saw orthogonal matrix. We also consider the effect of the Higgs asymmetry, showing that it lowers the upper bound on the neutrino masses in the so-called fully flavored regime where classic Boltzmann equations can be used. Imposing independence of the initial conditions contributes to lower the upper bound on neutrino masses as well. We study the conditions for the validity of the usual N_1-dominated scenario and for the applicability of the lower bound on the lightest right-handed (RH) neutrino mass M_1. We find that except for the two effective RH neutrino scenario, recovered for M_3 >>10^14 GeV, and for values M_2 < O(10^11 GeV), the final asymmetry is more naturally dominated by the contribution from N_2-decays. Finally, we confirm in a general way that going beyond the hierarchical limit, the effect of washout addition makes the lower bound on M_1 more stringent for (M_2-M_1)/M_1=O(0.1).

Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations

Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N-1-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.

A fuller flavour treatment of N_2-dominated leptogenesis

Abstract We discuss N 2 -dominated leptogenesis in the presence of flavour dependent effects that have hitherto been neglected, in particular the off-diagonal entries of the flavour coupling matrix that connects the total flavour asymmetries, distributed in different particle species, to the lepton and Higgs doublet asymmetries. We derive analytical formulae for the final asymmetry including the flavour coupling at the N 2 -decay stage as well as at the stage of wash-out by the lightest right-handed neutrino N 1 . Moreover, we point out that in general part of the electron and muon asymmetries (phantom terms), can completely escape the wash-out at the production and a total B − L asymmetry can be generated by the lightest RH neutrino wash-out yielding so-called phantom leptogenesis. However, the phantom terms are proportional to the initial N 2 abundance and in particular they vanish for initial zero N 2 -abundance. Taking any of these new effects into account can significantly modify the final asymmetry produced by the decays of the next-to-lightest RH neutrinos, opening up new interesting possibilities for N 2 -dominated thermal leptogenesis.

Successful type I leptogenesis with SO(10)-inspired mass relations

Abstract It is well known that thermal leptogenesis through the decays of the lightest right-handed neutrinos encounters serious difficulties when SO ( 10 ) -inspired mass conditions are imposed on the Dirac neutrino mass matrix and light neutrino masses are generated through the type I see-saw mechanism. We show that these can be circumvented when the production from the next-to-lightest right-handed neutrinos and flavor effects are properly taken into account. Some conditions on the low energy parameters have to be satisfied in order to explain the observed matter–antimatter asymmetry. In particular we find m 1 ≳ 10 −3 eV , where m 1 is the mass of the lightest left-handed neutrino and that non-vanishing values of the mixing angle θ 13 are preferred in the case of a normal fully hierarchical spectrum of light neutrinos.

An introduction to leptogenesis and neutrino properties

This is an introductory review of the main features of leptogenesis, one of the most attractive models of baryogenesis for the explanation of the matter–antimatter asymmetry of the Universe. The calculation of the asymmetry in leptogenesis is intimately related to neutrino properties so that leptogenesis is also an important phenomenological tool to test the see-saw mechanism for the generation of neutrino masses and mixing and the underlying theory beyond the Standard Model.This is an introductory review of the main features of leptogenesis, one of the most attractive models of baryogenesis for the explanation of the matter–antimatter asymmetry of the Universe. The calculation of the asymmetry in leptogenesis is intimately related to neutrino properties so that leptogenesis is also an important phenomenological tool to test the see-saw mechanism for the generation of neutrino masses and mixing and the underlying theory beyond the Standard Model.

Dark Radiation or Warm Dark Matter from long lived particle decays in the light of Planck

Abstract Although Planck data supports the standard ΛCDM model, it still allows for the presence of Dark Radiation corresponding up to about half an extra standard neutrino species. We propose a scenario for obtaining a fractional “effective neutrino species” from a thermally produced particle which decays into a much lighter stable relic plus standard fermions. At lifetimes much longer than ∼1 s, both the relic particles and the non-thermal neutrino component contribute to Dark Radiation. By increasing the stable-to-unstable particle mass ratio, the relic particle no longer acts as Dark Radiation but instead becomes a candidate for Warm Dark Matter with mass O ( 1 keV–100 GeV ) . In both cases it is possible to address the lithium problem.

The problem of the initial conditions in flavoured leptogenesis and the tauon N2-dominated scenario

Abstract We discuss the conditions to realise a scenario of ‘strong thermal leptogenesis,’ where the final asymmetry is fully independent of the initial conditions, taking into account both heavy and light neutrino flavour effects. In particular, the contribution to the final asymmetry from an initial pre-existing asymmetry has to be negligible. We show that in the case of a hierarchical right-handed (RH) neutrino mass spectrum, the only possible way is an N 2 -dominated leptogenesis scenario with a lightest RH neutrino mass M 1 ≪ 10 9 GeV and with a next-to-lightest RH neutrino mass 10 12 GeV ≫ M 2 ≫ 10 9 GeV . This scenario necessarily requires the presence of a heaviest third RH neutrino specie. Moreover, we show that the final asymmetry has to be dominantly produced in the tauon flavour while the electron and the muon asymmetries have to be efficiently washed-out by the lightest RH neutrino inverse processes. Intriguingly, such seemingly special conditions for successful strong thermal leptogenesis are naturally fulfilled within SO ( 10 ) -inspired models. Besides the tauon N 2 -dominated scenario, successful strong thermal leptogenesis is also achieved in scenarios with quasi-degenerate RH neutrino masses. We also comment on the supersymmetric case. We also derive an expression for the final asymmetry produced from leptogenesis taking fully into account heavy neutrino flavour effects in the specific case M 1 ≫ 10 12 GeV (heavy flavoured scenario), a result that can be extended to any other mass pattern.

Testing SO(10)-inspired leptogenesis with low energy neutrino experiments

We extend the results of a previous analysis of ours showing that, when both heavy and light flavour effects are taken into account, successful minimal (type I + thermal) leptogenesis with SO(10)-inspired relations is possible. Barring fine tuned choices of the parameters, these relations enforce a hierarchical RH neutrino mass spectrum that results into a final asymmetry dominantly produced by the next-to-lightest RH neutrino decays (N2 dominated leptogenesis). We present the constraints on the whole set of low energy neutrino parameters. Allowing a small misalignment between the Dirac basis and the charged lepton basis as in the quark sector, the allowed regions enlarge and the lower bound on the reheating temperature gets relaxed to values as low as ~ 1010 GeV. It is confirmed that for normal ordering (NO) there are two allowed ranges of values for the lightest neutrino mass: m1 (1−5) × 10−3 eV and m1 (0.03−0.1) eV. For m10.01 eV the allowed region in the plane θ13-θ23 is approximately given by θ2349°+0.65 (θ13−5°), while the neutrinoless double beta decay effective neutrino mass falls in the range mee = (1−3) × 10−3 eV for θ13 = (6°−11.5°). For m10.01 eV, one has quite sharply mee m1 and an upper bound θ2346°. These constraints will be tested by low energy neutrino experiments during next years. We also find that inverted ordering (IO), though quite strongly constrained, is not completely ruled out. In particular, we find approximately θ23 43°+12° log (0.2 eV/m1), that will be fully tested by future experiments.